Persistence is the key. Say your local paper drops TMW out of the blue, as part of some ill-considered cost-cutting measure. They get a lot of flak for doing so, but once the initial round of reader complaints die down, they’ve really got no motivation to reverse their decision.
But if they’re still getting complaints six months later… then maybe they reconsider.
There’s a directory of most of the altweeklies in the country here, along with email addresses. If you live in one of the affected cities, you’ll be able to find your paper there. Use this power for good and not evil!